a. Field of the Invention
This invention relates to a method and apparatus for creating a space curve and, more particularly, to a method and apparatus for space curve creation in which a three-dimensional space curve necessary for creating a free curved surface is created by smoothly connecting a three-dimensional sequence of discretely given points.
b. Description of the Related Art
A curved surface of a three-dimensional metal mold or the like on a design drawing is generally expressed by a plurality of section curves, but no profile data is shown for the shape of the area lying between a certain section curve and the next adjacent section curve.
In numerically controlled machining, it is essential that machining be carried out so as to smoothly connect these two section curves despite the fact that the profile between them is not given. In other words, this means that machining must be performed by generating the curved surface between the two section curves from such data as that indicative of the section curves, recording on an NC tape the data concerning the generated curved surface, and carrying out machining in accordance with commands from the NC tape. To this end, methods of generating a three-dimensional curved surface using data specifying several sections and section curves of a three-dimensional curved body have been proposed in U.S. Pat. No. 4,491,906 and U.S. Pat. No. 4,589,062.
FIGS. 9(a)-9(b) are views for describing a method of generating a three-dimensional curved surface associated with the prior art. The method includes giving three-dimensional curves (reference curves) 11a, 11b [see FIG. 9(a)] of a curved surface cut by a predetermined section, equally partitioning each of the reference curves 11a, 11b into N segments [see FIG. 9(b)], and connecting corresponding partitioning points by straight lines, thereby generating a curved surface CS [see FIG. 9(c)].
In this method of generating a three-dimensional curved surface, the reference curves, which are three-dimensional curves (space curves) must be specified. To this end, the conventional practice is to give a three-dimensional sequence of discrete points P1i (xi,yi,zi) (i=1, 2, . . . ) with regard to the reference curve 11a, as shown in FIG. 9(d), give a three-dimensional sequence of discrete points P2j (xj,yj,zj) (j=1, 2, . . . ) with regard to the reference curve 11b, and interpolate the space between points in each sequence by a cubic polynomial curve so as to smoothly connect each of the three-dimensional point sequences, thereby obtaining the space curves (reference curves).
In this conventional method of creating space curves, adjacent points are connected by a cubic spline curve (for example, see "Shape Processing Engineering [I]" by Fujio Yamaguchi, published by Nikkan Kogyo Shimbunsha, Chapter 3, pp. 80-85). A spline curve Si(t) between two points Pi-1, Pi is expressed by the following equation: ##EQU1## The space between the points Pi-1, Pi is spline-interpolated by varying t over a range of from 0 to 1. Here Pi-1, Pi signify position vectors and, assuming that Ci represents the distance between two points Pi-1, Pi and Pi' represents a unit tangent vector at the midpoint of a circular arc passing through three consecutive points. Ti signifies the product of Ci and Pi', namely Ti=CiPi'. Ti-1 similarly signifies the product of Ci and the unit tangent vector Pi-1', namely Ti-1=CiPi-1'. Eq. (1) is an induced equation of a Ferguson curve segment.
A problem encountered with this conventional calculation method of obtaining a three-dimensional spline is that considerable time is required for the calculation processing owing to the use of three-dimensional vectors. The amount of time required is particularly great when using a curved surface generating apparatus on the order of an ordinary personal computer.
Accordingly, an object of the present invention is to provide a method and apparatus for creating a space curve in which the space curve can be generated simply and processing time can be curtailed.